Here is something bizarre that Joao Magueijo and I have discovered. You can have a purely thermal big bang, all the way through, and reproduce the exact same deviation from scale-invariant primordial power spectrum, as observed in CMB data, without ANY fine-tuning or free parameters! This is more predictive (and falsifiable) than ANY inflationary (or non-inflationary) theory of early universe.
What’s the catch? The acoustic speed in the primordial plasma should suddenly diverge (i.e. become much faster than speed of light) at 4 orders of magnitude below Planck temperature. This is what my student and I had called Thermal Tachyacoustic Cosmology (TTC) before. What’s new is that there is a unique critical version of this model, with a geometric interpretation involving a membrane moving in a very special geometry (with two times 😜). Amazingly, it has a very sharp prediction for deviation from scale-invariance (n=0.9648) which matches CMB observations (n=0.9667 +/- 0.0040) to 3 significant digits!
So, there you have it! The most predictive theory of early universe, but it costs you a new time dimension 😀